Thermodynamic Processes and Formulas

Vocabulary flashcards covering the key thermodynamic processes (isobaric, isochoric, isothermal, adiabatic, and polytropic), including equations, variables, and diagram interpretations.

Isobaric Process in a $p,v$ Diagram

A process occurring at constant pressure ($p = \text{const}$), depicted as a horizontal line on a $p,v$ diagram.

Isochoric Process in a $p,v$ Diagram

A process occurring at constant specific volume ($v = \text{const}$), depicted as a vertical straight line on a $p,v$ diagram.

Isothermal Process ($T = \text{const}$)

A thermodynamic change where temperature remains constant and there is no change in internal energy ($\Delta u = 0$), meaning supplied heat equals work; expansion occurs by adding heat, and compression by removing heat.

Heat and Work Formula for an Isothermal Process

$q_{1,2} = w_{1,2} = R \cdot T \cdot \ln\left(\frac{v_2}{v_1}\right)$, where $R$ is the gas constant ($\text{J/(kg}\cdot\text{K)}$), $T$ is absolute temperature ($\text{K}$), and $v_1, v_2$ are specific volumes ($\text{m}^3\text{/kg}$).

Adiabatic Process ($q = 0$)

A process where no heat exchange occurs with the surroundings due to high speed or good insulation; work performed equals the change in internal energy.

Adiabatic Expansion vs. Isothermal Expansion Work

Because the adiabat curve is steeper than the isotherm curve in a $p,v$ diagram, the work done during adiabatic expansion is less than the work done during isothermal expansion.

Adiabatic Equation of State

$p \cdot v^\kappa = \text{const}$, where $\kappa$ is the adiabatic exponent, which equals $1.4$ for air.

Work of an Adiabatic Process ($w_{1,2}$)

The work done by $1\,\text{kg}$ of gas, given by $w_{1,2} = c_v \cdot (T_1 - T_2)$, where $c_v$ is specific heat at constant volume ($\text{J/(kg}\cdot\text{K)}$) and $T_1, T_2$ are the initial and final temperatures ($\text{K}$).

Polytropic Process

A general thermodynamic process defined by $p \cdot v^n = \text{const}$, occurring with heat exchange and temperature changes, situated between an isotherm and an adiabat.

Polytropic Exponent ($n$)

An exponent determined experimentally for a polytropic process, which for air falls within the range $1 < n < 1.4$.

Heat Transferred in a Polytropic Process ($q_{1,2}$)

The heat exchanged during a polytropic process, calculated as $q_{1,2} = c_v \cdot \left(\frac{n - \kappa}{n - 1}\right) \cdot (T_2 - T_1)$.

Area Under the Curve in a $p,v$ Diagram

The geometric area beneath the process curve on a $p,v$ diagram, which represents the executed work.